What is the best way to go. I saw there is a Strauss Track on the map leaving out of Heidelburg following up the Neckar River to just south of Rothenburg. But was wondering if there are taxis or other methods in the area that can take you from around Eberbach to Rothenburg.
I'd suggest you use the German Rail website to find train schedules. For regional trains, you can take the S-Bahn from Heidelberg (or Eberbach) to Osterburken, then a regional train to Würzburg, and then the standard regional connection from Würzburg to Steinach to Rothenburg. Time is about 4 hours. Runs every two hours, at 8:55, 10:55, 12:55, etc. You almost have to go into Rothenburg from Steinach, to the east. You could get off the Osterburken to Würzburg train somewhere like Bad Mergentheim or Lauda and take a bus in from the west, but I don't think it is any faster. You could also go by express train (ICE/IC/EC), but those routes are less direct to Würzburg, don't save much time, and cost more. A VRN ( Verkehrsverbund-Rhein-Neckar) ticket from Heidelberg to Osterburken to Würzburg will cost you €8,50 per person. The Bahn ticket from Würzburg to Steinach to Rothenburg, €11,70. From this page you can access the track plans for Baden-Württemberg (Heidelberg to Würzburg) and Bayern (Würzburg to Rothenburg).